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SOHCAHTOA Ratios Demo

SOHCAHTOA Ratios Demo
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2015-04-28 22:13
AngleTrigonometryGeometric Construction
This example demonstrates how the ratios of sine, cosine, and tangent change in a right triangle. It involves core math concepts like trigonometric functions, angles, and side relationships in right triangles. Constructed using GeoGebra commands such as Intersect, Point, Segment, Rotate, Angle, Line, OrthogonalLine, and Distance to build the figure and calculate ratios. Suitable for high school students learning and understanding the basic properties of trigonometric functions, ideal for classroom instruction or self-exploration.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → C
  3. Segment(A, C) → Adj
  4. Rotate(C, α, A) → C'
  5. Angle(C, A, C') → β
  6. Line(A, C') → a
  7. OrthogonalLine(C, xAxis) → c
  8. Intersect(a, c) → B
  9. Distance(A, B) → AB
  10. Segment(A, B) → Hyp
  11. Segment(C, B) → Opp
  12. Segment(A, C) → f
  13. Angle(B, C, A) → γ

AI Drawing Prompt Reference

Draw a right triangle ABC with A as the right angle, C as the vertex, and B on the hypotenuse. Start by drawing the intersection of the x-axis and y-axis as point A, then take point C on the x-axis and connect AC to form the base. Rotate point C around A to form C', and measure the angle ∠C'AC as β. Draw a line a through A and C', and construct a perpendicular line c from C to the x-axis, intersecting at point B. Connect AB and BC to form the hypotenuse and opposite side, respectively. Finally, measure the angle ∠BAC as γ.
The prompt above was compiled from the original drawing commands and is for reference only.